Low-energy super Gamow–Teller (LeSGT) and anti-LeSGT transitions

Abstract

The LS-closed doubly-magic nuclei (DMN) $^{4}_{2}\mathrm{He}_{2}$, $^{16}_{\;\, 8}{\mathrm{O}}_{8}$, and $^{40}_{20}{\mathrm{Ca}}_{20}$ behave as inert cores for Gamow–Teller (GT) excitations. It is known that GT transition strengths from nuclei with DMN + identical two-nucleon particles (2p) to nuclei with DMN + proton-neutron particles ($\pi p$-$\nu p$), i.e., $^{6}_{2}{\mathrm{He}}_{4}\rightarrow ^{6}_{3}{\mathrm{Li}}_{3}$, $^{18}_{\;\, 8}{\mathrm{O}}_{10}$ (or $^{18}_{10}{\mathrm{Ne}}_{8}$) $\rightarrow ^{18}_{\;\, 9}{\mathrm{F}}_{9}$, and $^{42}_{20}{\mathrm{Ca}}_{22}$ (or $^{42}_{22}{\mathrm{Ti}}_{20}$) $\rightarrow ^{42}_{21}{\mathrm{Sc}}_{21}$, concentrate in the lowest GT states called the Low-energy Super GT (LeSGT) states. On the other hand, we notice that the GT strengths from nuclei with DMN + identical two-nucleon holes (2h) to nuclei with DMN + proton-neutron holes ($\pi h$-$\nu h$), i.e., $^{14}_{\;\, 6}{\mathrm{C}}_{8}$ (or $^{14}_{\;\, 8}{\mathrm{O}}_{6}$) $\rightarrow ^{14}_{\;\, 7}{\mathrm{N}}_{7}$, and $^{38}_{18}{\mathrm{Ar}}_{20}$ (or $^{38}_{20}{\mathrm{Ca}}_{18}$) $\rightarrow ^{38}_{19}{\mathrm{K}}_{19}$, concentrate in the second GT states. Accordingly, the lowest GT states, which can be called the anti-LeSGT states, are poorly excited. We find that this seesaw-like GT strength distributions in the 2p and 2h systems are the key to understand the hindered $\beta $ decay of $^{14}$C. The origin of the “Seesaw Mechanism” is analyzed by means of shell-model (SM) calculations.